The variation in these three QPM parameters can be denoted by the motion of a vector \(\mathbf {Q}=(\Xi \cos \phi _{d},\Xi \sin \phi _{d}, \Delta \Gamma /2)\)  in the parameter space [See Figs. REF (a,b)]. When the intensity of the pump wave is strong enough, which can be termed as an undepleted wave, the system can be represented by a spin-1/2 system, and the \(\mathbf {Q}\)  vector can be equivalent to the time-dependent magnetic field [1]}. The initial conditions for the three waves are defined by the initial intensities of the three waves; i.e., \(I_{j}=|q^{(0)}_{j}|^2\) . According to the rescaling definition in Eq. (REF ), the sum of \(I_{j}\)  automatically satisfies
\(I_{1}+I_{2}+I_{3}=1.\) 
